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Sensors and Materials, Vol. 36, No. 9 (2024) 3817–3841
MYU Tokyo
S & M 3769

Servo Sensor Signal Utilization in Machine Tool Condition
Monitoring and Fault Diagnosis
Cheng-Kai Huang,1 Chun-Hao Chen,2 Kun-Ying Li,3* and Shih-Jie Wei4
1Department of Mechanical Engineering, National Chin-Yi University of Technology,

No. 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 41170, Taiwan

2Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology,

No. 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 41170, Taiwan

3Department of Intelligent Automation Engineering, National Chin-Yi University of Technology,

No. 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 41170, Taiwan

4Intelligent Machinery Technology Center, Industrial Technology Research Institute,195, Sec. 4, Chung Hsing Rd., Chutung, Hsinchu 310401, Taiwan(Received June 11, 2024; accepted August 30, 2024)

Keywords: data-driven sensing, status estimation, fault diagnosis

Because of changing consumer habits, manufacturing processes are shifting from mass
production to small-batch production, which is making machining more complex and increasing
demands for precision and stability. Machine tools, and thus machining accuracy, are affected byfactors such as temperature and cutting load. Existing online estimation techniques often require
the installation of additional sensors at specific locations, an approach that has cost andreliability issues, thus limiting industry’s acceptance of these techniques. In practice, mostmanufacturers rely on offline detection methods, meaning that machining accuracy deviations
can take some time to detect. In this study, we developed a technology for monitoring the statusof machine tools; this technology, rather than requiring the installation of sensors, uses servo
sensor signals to estimate accuracy, diagnose faults, and make recommendations regarding
cutting depth parameters. The proposed method leverages a small number of experiments
combined with extensive finite element analysis to construct a big data database, followed by thesensitivity and regression analyses of the generated database to produce an estimation model that
evaluates machine tool conditions through servo feedback. The results showed that using linear
regression to estimate the machine tool’s status achieves good accuracy and that linear regression
is easier to implement for real-time compensation. Ultimately, these results can enhance
production efficiency and machining accuracy, as well as prevent unforeseen breakdowns.

1.

Introduction

The machining industry is moving toward a digital smart production and manufacturingmodel. Machine manufacturers provide value-added services in their products, which areachieved through a wide range of software features such as conversational operation interfaces
for shortening process preparation times, optimizing processes, or the utilization of Internet of*Corresponding author: e-mail: likunying@ncut.edu.twhttps://doi.org/10.18494/SAM5175

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 36, No. 9 (2024)

Things technologies to monitor equipment for pre-emptive maintenance. These features
facilitate the realization of smart plants. Such value-adding software typically replaces humanoperations with sensors and communication technologies and thus enhances performance andlowers costs by reducing labor requirements. To enter or remain in high-end machine tool
markets, machine tool manufacturers have changed their industry development strategies byshifting from the research and development mindset of the past, which focused on improving thespecifications and performance of single machines, toward providing application-end solutions
and after-sales service systems that meet customer needs and address actual problems inproduction.
For terminal processing plants, changes in consumer habits have led to a transition from mass
production to small-batch production. Consequently, machining behaviors have grownincreasingly complex. To respond to shortening product lifespans, the adaptability and stability
demands in machining have become greater. The most competitive vendors are those who
respond fastest to market demands. The selection of machining parameters through outdated
practices such as the onsite staff’s trial and error results in large numbers of rejects, and thematerial and time costs do not support small-batch production. Machining businesses must finda way to automate their analysis of the machine state and adjust depth-of-cut parameters toensure high product efficiency. Precision is a key indicator of the performance of machine tools,
which can be compromised by factors such as temperature changes, the cutting load, and wear.
Approximately 20% of the yearly operating costs of machining businesses go toward machine
maintenance and repairs, and 50% of those expenses are spent on precision machine calibration.
Therefore, given the current requirements for high precision and efficiency, the accuracy ofmachining equipment must be estimated and its faults diagnosed; the advance detection ofabnormalities and the elimination of problems result in less machine downtime while improving
machine utilization, efficiency, and production value.
Two major components of a machine tool are its transmission shaft and rotating axis; theirperformance and precision determine the production efficiency and machining precision. As thetotal machining time performed by a machine increases, changes occur in the precision andhealth (backlash, precompression, and abnormalities) of the transmission shaft (straightness
variation) and rotating axis (axial thermal elongation), compromising the precision of themachine. Moreover, an abnormality in one of these shafts that is not detected in time may lead toa considerable drop in machining quality, resulting in a massive number of defective products
and even a shutdown. Some technologies that can detect the machine status in real time havebeen employed for precision compensation, fault diagnosis, and parameter recommendations,but these technologies require the installation of additional sensors in specific locations; inpractice, mechanical designs or machining constraints often prevent the installation of suchsensors, meaning that the desired physical measurements must instead be calculated indirectly.
The cost and lifespan of sensors may also lower system reliability to such a degree that amachining business may be unable to tolerate; at this stage, most businesses rely on offline
detection, preventing punctual adjustment when changes in precision are detected. Furthermore,even with regular shutdowns (e.g., once per month) for maintenance and repairs, a sudden
malfunction that cannot be prevented or resolved in a timely fashion may occur.

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The objective of the present study was to develop a technology for monitoring the conditionof machine tools. This technology, rather than requiring the installation of additional sensors,
uses servo sensor signals to estimate accuracy, diagnose faults, and make recommendations for
cutting depth parameters. The proposed method involves the extensive finite element analysis of
basic parameters obtained through experiments or mechanical designs, with this analysis being
achieved through the simulation of the relationship between the inputs (such as the servo
feedback signal) and outputs (temperature, abnormality, and torque) under various conditions(including environmental and movement conditions). A small number of sampling experiments
were performed to evaluate the accuracy of the simulations and correct the simulation conditions
to improve the fit of the simulation results to actual machine statuses. This facilitated theestablishment of a big data database and estimation model. This estimation model evaluates thecondition of machine tools by analyzing servo feedback signals—such as stator temperature,
motor speed, motor current, and motor torque signals—to estimate the thermal displacement
and component stress and thus diagnose faults. The proposed system can enhance production
efficiency and machining accuracy and prevent unforeseen breakdowns and subsequent impacts
on manufacturers’ production capacity and delivery time. Digital predictions based on servo
feedback may be less accurate than sensor detections, and machines may deviate from the digitalmodel over time, resulting in a decrease in prediction accuracy; however, the proposed approachovercomes the issues of an inability to install sensors owing to the spatial and design restrictionsof machines and the possibility that sensor installation will compromise system reliability(sensors may fail) and increase costs. The digital model can be updated by comparing its resultswith actual machining results and then calibrating it to maintain high prediction accuracy.
In the relevant literature, researchers have proposed various approaches to the autonomous
care of machining equipment through accuracy estimation and fault diagnosis. Research on
accuracy estimation has included the study of Kong,(1) who performed simulation experiments
and optimized the thermal characteristics of a machine tool by establishing a heat transfer modelthat could be used as a foundation for enhancing machining precision. Ma et al.(2) measured thethermal errors of vertical machining centers by collecting experimental data and analyzing theimpact of these errors on the machining output; their study offers a practical reference for
optimizing the performance of vertical machining centers. Tangjitsitcharoen(3) compared theabilities of neural network and regression analysis models to predict the variation in thestraightness of a transmission shaft during computer numeric control (CNC) turning andpresented the advantages and limitations of applying machine learning techniques inmanufacturing processes. Czerwinski et al.(4) utilized machine learning to monitor the current ina brushless DC motor and calculate its temperature changes, thereby achieving sensor-lesstemperature estimation. In research on fault diagnosis, Douglas et al.(5) proposed an algorithm
that uses wavelets to analyze transient motor current characteristics and, for the transient
operations of induction machines, applied the algorithm to detect and analyze abnormalities on
the basis of waveform features. Kar and Mohanty(6) monitored gear vibrations by performing
current signature analysis and wavelet transform; in addition to the monitoring of gear condition,
their detailed waveform-transform-based analysis provided a reference for evaluating equipment
health. Dambrauskas et al.(7) reported an approach for monitoring and diagnosing the condition

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Sensors and Materials, Vol. 36, No. 9 (2024)of bearings in induction motors; their approach, based on cloud services and artificial neuralnetworks, integrates cloud computing with deep learning. Proposing an approach for speed andfailure detection in brushless DC motors, Medeiros et al.(8) presented a novel approach fordetecting speed and failures in brushless DC motors using chaos theory. Their proposed method
leverages chaotic behavior to enhance the detection accuracy of both speed variations and motor
failures. By employing a chaotic oscillator, the technique effectively identifies irregularities in
the motor’s operation, which are indicative of potential failures. They demonstrated the method’s
efficacy through extensive experimentation, showing significant improvements in detection
precision. The results highlight the potential of chaos-based systems in industrial applications
for the real-time monitoring and maintenance of brushless DC motors, ensuring greater
reliability and operational efficiency. Medeiros et al.(8) employed the chaotic behaviors exhibitedby a motor to monitor the motor’s reliability. Azeem et al.(9) have introduced an advanced AI
feature called the AI Servo Monitor. This tool collects high-speed data related to machine tool
feed and spindle control. It employs deep learning techniques on this data to display anomaly
scores reflecting the current condition of machine components. During normal machine
operation, the AI Servo Monitor uses motor torque data to train the model, identifying
characteristics that indicate normal torque conditions. In real-time operation, the AI Servo
Monitor compares incoming torque data with the normal state, calculating and displaying
anomaly scores. This functionality enables machine tool operators to detect early signs of feedor spindle failures. By alerting operators to perform maintenance before any failures occur, theAI Servo Monitor helps enhance machine availability. Totu et al.(10) created the Intelligent
Thermal Shield (ITS) system to tackle thermal displacement problems. This system utilizes
sensors strategically placed in areas prone to thermal displacement to gather data. ITS
compensates the rapid and dynamic thermal displacement occurring during axis rotation by
analyzing surface displacement data in relation to the thermal response of the rotational speed.
In contrast, for slower, more uniform thermal displacement due to environmental temperaturechanges, ITS uses temperature application formulas for compensation. By conducting
experiments and observations, Totu et al. refined thermal displacement compensation using thecollected sensor data, ensuring consistent and precise machining performance across different
environmental conditions. Liang et al.(11) introduced a novel system for predicting thermal errors
in heavy-duty CNC machines. This system employs long short-term memory (LSTM) networks
and a fog–cloud architecture. The findings demonstrated that, compared with traditional
methods, this new system reduces data transfer by 52.63% and enhances machining precision by
46.53%. Gui et al.(12) explored the prediction and control of spindle system thermal errors,
proposing a new mist–edge fog–cloud system (MEFCS). This system utilizes Bi-LSTM
networks and cosine and sine gray wolf optimization (CSGWO) algorithms. The results indicatedthat the accuracy of tooth profile deviation improved from ISO level 5 to ISO level 3 with theimplementation of the MEFCS. Guo et al.(13) investigated the spatiotemporal correlation of datain the static thermal deformation modeling of CNC machine tools using a hybrid CNN-LSTM
model with spatiotemporal correlation (ST-CLSTM). The ST-CLSTM model demonstrates
excellent prediction performance, robustness, and generalization ability. It surpasses othercomparison models in terms of prediction accuracy, generalization, and robustness in threeSensors and Materials, Vol. 36, No. 9 (2024)

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different directions, as evidenced by thermal error studies conducted under various conditions,
including varying spindle speeds and ambient temperatures. Kuo et al.(14) presented a method of
autonomous optimization using a bidirectional gated recurrent unit (GRU) to accurately predict
manufacturing errors. Their approach utilizes an optimized automatic logistic random generator
time-varying acceleration coefficient particle swarm optimization (LRGTVAC-PSO) method toenhance a branch-structured bidirectional GRU neural network. The results indicated that thebidirectional GRU outperforms other optimized algorithms in terms of prediction accuracy,
achieving a three-axis average accuracy of 0.945. This demonstrated the superior performanceof their proposed method in time-related prediction tasks. Kuo et al.(15) employed advanced
algorithms to predict the thermal displacement of machine tools. Their method utilizes anensemble model that combines LSTM with a support vector machine (SVM). The experimental
results indicate that the LSTM–SVM hybrid model outperforms other machine learning methods
in prediction accuracy. Specifically, the prediction RMSEs were reduced to 2.13, 3.91, and 2.04,
with an overall mean RMSE of 2.69. This performance surpasses those of the standalone LSTM
and SVM models, which had mean RMSEs of 3.28 and 2.97, respectively. Liu et al.(16)
investigated the relationship between spindle thermal errors and temperature fluctuations,aiming to develop a reliable and efficient spindle thermal displacement modeling method. They
compared three modeling approaches: LSTM, multiple linear regression (MLR), andbackpropagation neural network (BPNN). The results indicated that, particularly at high spindle
rotation speeds, the ANN-based models (LSTM and BPNN) significantly outperformed the
MLR method. Additionally, across all spindle operating conditions, the LSTM model showed alower root mean square error (RMSE) than the BPNN model. The proposed spindle thermal
error prediction technique was validated at spindle rotation speeds of 3000, 6000, and 9000 rpm.
Liu et al.(17) conducted a study on spindle systems, focusing on thermal error modeling andcompensation based on the error mechanisms of these systems. They employed the VMD-GWLSTM network, the VMD-LSTM network, and RNN for their methods. The results showed thatthe compensation rates for the VMD-GW-LSTM network model were 77.78% for two of theexperimental setups and 75.00% for the third setup. Additionally, the VMD-GW-LSTM networkmodel outperformed the VMD-LSTM network and RNN models in both prediction andcompensation analyses. Nguyen et al.(18) focused on reducing thermal errors in workpieces bydeveloping a thermal deformation prediction model using an artificial neural network
specifically applied to a three-axis vertical CNC milling machine during cutting processes.
Their method employs LSTM with Pearson’s correlation coefficients for feature selection. Theirstudy results illustrated the effectiveness of a real-time error correction system when an LSTM
neural network is used as the temperature error prediction model. During an 8 h cutting
experiment, real-time error compensation significantly reduced thermal errors—from 7 to 3 µm
on the X-axis, from 74 to 21 µm on the Y-axis, and from 64 to 20 µm on the Z-axis—thereby
enhancing the precision of the workpiece dimensions. Zeng et al.(19) developed a method ofpredicting thermal error in machining using a sequence-to-sequence LSTM network with anattention mechanism (SQ-LSTMA) integrated into an edge cloud system. Their results indicatedthat the SQ-LSTMA model surpasses other networks such as BP, RNN, and standard LSTM in
prediction accuracy and convergence rate, achieving an accuracy of 99.02%. Additionally, the3822

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attention mechanism significantly reduces computation time, making SQ-LSTMA faster andmore efficient than traditional methods. Ji et al.(20) presented a proactive anomaly detection
framework for robot navigation using multisensor fusion. Their approach integrates data fromvarious sensors to enhance the reliability and accuracy of anomaly detection during navigation
tasks. Their results demonstrated that the proposed method effectively identifies potential
anomalies before they impact the robot’s performance, thereby improving the safety androbustness of autonomous navigation systems.
These papers offer various approaches and techniques for estimating the accuracy of anddiagnosing faults in machine tools and their components. The techniques can be divided into
two principal categories: those involving the direct acquisition of necessary physical quantities
through the installation of additional sensors and those involving the use of sensorlesstechnology based on current signals to determine heat generation and thus estimate temperatureand motor efficiency. The strengths of both these categories were combined in our study. Our
proposed approach is to employ existing sensors in a servo motor (including sensors for statortemperature, rotation speed, current, and torque) to estimate temperature, thermal deformation,and component stress conditions and to perform fault diagnoses; these actions will ultimately
improve machining precision and prevent unforeseen failures. The proposed approach canenhance system reliability without requiring the installation of additional sensors and thus will
reduce costs while providing a higher estimation accuracy than that offered by other sensorlessprediction technologies. Our system meets the machining demands of the machine tools industry
and can help manufacturers improve machining efficiency and accuracy while avoiding losses in
production value owing to sudden failures.

2.

Experimental Equipment and Methods

2.1

Equipment for analysis and experiment

The thermal deformation of machine tools is mainly caused by environmental changes andthe thermal expansion of structural materials owing to thermal energy. In this study, we
conducted experiments combined with extensive finite element analysis to build a database anda model for estimating thermal deformation. Figure 1(a) is the schematic diagram of theexperimental machine tool. The model of the machine tool is IT-25, which is a lathe structure
and was developed and designed by the Industrial Technology Research Institute in Taiwan.
Figure 1(b) shows a specifications table of the lathe machine.
The PT100 resistance temperature detector was used to measure the temperature changes,
and the eddy current sensor AEC S-06 was used to measure the thermal deformations. The
temperature changes and the thermal deformations of the lathe were recorded by GRAPHTEC’s
GL820 data logger for subsequent analysis. Figure 2 shows the measurement equipment.
2.2

Prediction methodology

Regression analysis is mainly used to analyze the relationship between one or more
independent and dependent variables. The regression analysis can be divided into simple

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(a)
Fig. 1.

(b)(Color online) The experimental machine tool: (a) IT-25 lathe and (b) specifications table of the lathe.

(a)

(b)

(c)
Fig. 2.

(Color online) Measurement equipment: (a) signal recorder (GL820); (b) eddy current sensor; and (c) PT100.

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regression and multiple (or complex) regression. Simple regression is an analytical method with
only one independent variable and one dependent variable in the regression equation to represent
the relationship between the independent variable and the dependent variable. However, multiple
regression is an analytical method that includes two or more independent variables in the
regression equation, allowing for the understanding of the response levels or quantities of thedependent variables on the basis of the levels or quantities of the independent variables.
In this study, the room temperature was controlled in accordance with the spindle load andexperimental conditions. Consequently, multiple regression was employed to determine theappropriate supply oil flow rate for the spindle under varying cooling demands. Multiple
regression can be expressed asyt   0  1x1t   2 x2t    n xnt   t ,(1)

where yt is a dependent variable, xit are independent variables, β0 is a constant, β1 to βn areregression coefficients, and εt is the error.
After performing the regression analysis, a regression equation was obtained, allowing therelationship between the dependent and independent variables to be determined. In this study, an
F-test was then used to evaluate the prediction accuracy and significance of the developed
regression equation. The following assumptions apply to the F-test:
H0： 1   2     n  0
H1：  k  0 (where 0 < k < p ),(2)

where p represents the number of independent variables. The following statistical test quantity isadopted to evaluate the prediction and significance of the regression equation.
F* =

MSR
MSE

(3)

Here, MSR and MSE represent mean square regression and mean square error, respectively. If
the significance level is set as α, the determination rule of significance is as shown below.
• If F* ≤ F (1 − α; p − 1, n − p), the significance does not exist. The assumption H0 is valid.
• If F* > F (1 − α; p − 1, n − p), the significance exists. The reliability of the regression equation
can be accepted. The assumption H1 is valid.
F represents the critical value obtained from the F distribution table at a specific significancelevel α. The coefficient of multiple determination is used to represent the goodness of fit of theregression model and is defined as
R2 

SSR
SSE
1
,
SST
SST

(4)

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where SSR, SSE, and SST represent the sum of squares for regression, the sum of squares forerror, and the total tum of squares in statistics, respectively. The range of R2 is 0 ≤ R2 ≤ 1. The
value of R2 indicates the strength of the relationship between the dependent and independent
variables. A high R2 value suggests that the dependent variables can be accurately predictedfrom the independent variables in the regression equation. R2 is defined as the ratio of thevariance explained by the regression model to the total variance of the dependent variable yi. A
large R2 means that the regression model explains a greater proportion of the total variation.
2.3

Simulation analysis and experiment

The commercial software ANSYS Fluent was employed to simulate the flow field,
temperature distribution, and corresponding thermal deformations within the computational
domain. In this study, the finite volume method and fluid–solid coupling calculations were
utilized to model the flow field within the lathe structure, as well as the temperature distribution
and associated thermal deformations. To ensure the uniformity of the flow field within the lathe
structure, a low flow velocity was maintained, and the fluid in the flow field was assumed to beincompressible. For model simplification, the Navier–Stokes equations and the energy equation
for a three-dimensional incompressible fluid are presented as follows:
U j
x j

 (U iU j )
x j
and



 0� , j = 1, 2, 3

  U i  u u 
1 P gi  (T  T ) i j, x j
x j  x j

 TU jx j    v T  T'u  ,
x j  Pr x j

j



(5)

where Uj, T, and P are the averages of velocity, temperature, and pressure, respectively. Under
the Boussinesq assumption, the buoyancy effect is considered, and β is the thermal expansion
coefficient. With a turbulent closure model, the turbulent stress −ui u j and turbulent heat flux
−T ′u j can be obtained asv  T 2
ui u j  2vt Sij  k ij  T u j  t ,Prt  x j 
3(6)

where vt and Prt are the turbulent kinematic viscosity and turbulent Prandtl number, respectively.
k is the kinetic turbulent energy, where k = u x2 + u 2y + u z2 / 3 , and δij is the Kronecker function.
The turbulent closure problem is computed using the k-ε model, where the turbulent stress and3826

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turbulent heat flux can be obtained using the kinetic turbulent energy and turbulent dissipation
equations, respectively.
The conditions for simulation analysis are shown in Fig. 3. The power of the spindle motor
measured using the power meter was 500 W. In the study, the heat generated by a hydrauliccylinder, turret, and the front and rear bearings were 68 ℃, 50 W, 138 W, and 120 W,
respectively, as shown in Fig. 3(a). In Fig. 3(b), the air flow velocity in the environmental flow
field measured by the flow meter was 8.2 m/s, and the air flow rate close to the spindle motor
end was 0.3 m/s. The number of grids in the simulation analysis was approximately 12.7 million,
as shown in Figs. 3(c) and 3(d).
The conditions of the experiments were based on the lathe usage status in the test. The
experimental conditions are shown in Table 1 below.

(a)

(b)

(c)

(d)

Fig. 3. (Color online) Conditions for simulation analysis: (a) heat generated, (b) air velocity, (c) mesh, and (d)simulation.

Sensors and Materials, Vol. 36, No. 9 (2024)

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Table 1
Experimental conditions.
1

2

Experimental
test conditions

No operation
Room temp.+15 ℃
Constant temp. measurement
Spindle area/fan ON

Spindle operation/stop 8/2 hConstant room temp.
Constant temp. measurement
Spindle area/fan ON

SensorEddy current
PT100

Eddy current
PT100

2.4

3
Spindle operation/stop 8/2
hours
Room temp.+15 ℃
Constant temp. measurement
Spindle area/fan ON
Eddy current
PT100

Equipment monitoring and accuracy estimation

The machining industry has already begun moving toward a digital smart production andmanufacturing model, and manufacturers can add value to systems through a wide range ofsoftware services that replace human behaviors with sensors and communication technologies
and thus enhance the performance and lower the costs by reducing the demand for labor. A
system for monitoring the precision and condition of metal cutting equipment, which caneffectively aid operators in diagnosing equipment condition and enhancing machining accuracy,
was developed in this study. The modules of this system include transmission shaft and rotating
axis condition detection functions, enabling the user to estimate and compensate forabnormalities, component stress, backlash, straightness, and axial thermal expansion without
needing to install additional sensors. The machine tool controller is employed to acquire theservo feedback information necessary for digital estimation, thus overcoming the limitations of
sensors and effectively lowering the barriers to entry for operators wanting to upgrade theirmachinery intelligence. The condition monitoring and precision self-care modules of thedeveloped system perform immediate monitoring and failure prevention by capturing signals,
computing features, and determining conditions on site and in real time. This enables the daily
assessment of a machine’s condition during its warm-up, proactive maintenance scheduling,compensation for backlash, and real-time monitoring of temperature and thermal displacement(including rotating axis extension and transmission shaft straightness variations) during themachining process to maintain stable quality and prevent overheating failures. The three mainfunctions of the proposed system are as follows.
• Precision Estimation and Compensation: The transmission shaft backlash, straightness
variation, and thermal extension of the rotary shaft are estimated to assist the user inprecision compensation and thereby maintain stable machining precision and reduce themachine warm-up time.
• Cutting Depth Parameter Assistance: Real-time estimates and displays of motor, bearing, andnut loads are provided, enabling the user to adjust the maximum cutting depth for roughmachining on the basis of the degree of component stress, enhancing machining efficiency
and maintaining machining quality.
• Prevention of Sudden Failures: The transmission and rotating axis temperature andabnormality estimation modules can be implemented to prevent overheating failures duringmachining and provide early warnings of abnormalities (indications of future failure even if
the machine remains operational) to help the user schedule maintenance.

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These modules do not require the installation of sensors in machines, which can be impossible
because of the difficulty in placing sensors in older machines or other reasons, and instead draw
upon feedback information from the machine tool controller to perform state monitoring,
precision estimation, and compensation. The modules can help operators maintain consistentquality and reduce waste. The development of these modules began with the acquisition of basic
component parameters through experiments or from the components’ mechanical designs. Input
and output relationships were then simulated under various conditions (environmental andoperational) using finite element analysis software. The extensive digital simulations were thensampled in several experiments in which the accuracy of the simulation analysis was evaluated,
providing feedback regarding how the simulation conditions should be adjusted such that thesimulation results would more closely match the actual state of the machinery. This processfacilitated the creation of a large-scale database. Finally, the sensitivity analysis of the estimation
targets (temperature, thermal displacement, rigidity, and health state) was performed using servo
feedback information such as stator temperature, speed, current, and torque, and the results
revealed the parameters that have the strongest impact for regression analysis. The predictivemodel was converted into mathematical polynomials suitable for real-time calculations. The
transmission and rotating axis estimation technology developed in this study assumes that thetransmission and rotating axis primarily comprise motors, bearings, and nuts. The first step inthis study was the establishment of methods of estimating the condition of these three individualtypes of component; these methods were then integrated into the evaluation of the transmission
and rotating axis.

3.

Results and Discussion

3.1

Motor state detection technology

In this section, we describe in detail the development of the motor state prediction technology.
The process was as follows. First, the copper loss, iron loss, transient temperature, and efficiency(torque–rotational speed–efficiency relationship) of a motor were plotted in accordance with themathematical relationship between electromagnetism and heat. Second, the plot was employed
as the basis for establishing a technique for motor heat effect analysis; the motor efficiency plot
was used to illustrate the efficiency for various rotational speeds and torques, enabling the
calculation of the heat generated by the motor while it was in operational and the heat transmitted
to the surroundings. Motor heat calculations can help operators protect their motor fromoverheating, which would otherwise cause thermal displacement in the screws and structure of
the machine tool. The developed module for motov status self-detection was modeled as follows(as shown in Fig. 4).
1. The basic parameters of the motor were acquired from the manufacturer or measured by the
researchers. The current, voltage, resistance, and power factor (PF) under no-load and loadconditions were then obtained using a power analyzer (a digital oscilloscopic power meter)
and employed to establish a model of the motor.
2. Data were imported into ANSYS for analysis and to obtain theoretical curves for rotational
speed, torque, and efficiency.

Sensors and Materials, Vol. 36, No. 9 (2024)

Fig. 4.

3829(Color online) Motor status self-detection module: model construction process.

3. The data obtained by preexisting sensors—such as motor speed, motor current, and statortemperature data—were received through the controller and used as inputs to improve theprediction accuracy.
4. The servo motor temperature was estimated from the current, rotational speed, and statortemperature. During model verification, multipoint temperature sensors were installed on theoutside of the motor to ensure the accuracy of the motor temperature simulation results and toprovide feedback that could be used to correct the simulation conditions and improve theprediction accuracy.
5. During fault diagnosis, the ideal torque was reverse-calculated from the motor speed andcompared with the measured torque. Abnormalities in the motor status were detected fromthe difference between the ideal and actual torques. The accuracy of the motor abnormality
determinations made by the model was verified by adding an accelerometer to the motor.
Once large amounts of simulation data had been acquired and the sampling verifications andrevisions had been performed, the simulation and measured data were subjected to sensitivity
analysis to evaluate the relationship between the servo feedback and the surface temperature of
the motor flange. The five-axis machine tool developed by the Industrial Technology ResearchInstitute’s Smart Machinery Technology Center was employed as the model of interest in thisstudy. The results revealed that the surface temperature of the motor flange could be expressedas the following function of the stator temperature:
TMotor  CST 0  CST 1Tstator ,

(7)

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Sensors and Materials, Vol. 36, No. 9 (2024)

where TMotor is the surface temperature of the motor flange, CSTi is the ith-order temperature
constant of the motor stator in relation to the flange surface, and Tstator is the motor statortemperature. The relationship expressed in Eq. (1) is illustrated in Fig. 5.
3.2

Bearing and nut status detection

Most bearings and nuts on the market are not equipped with sensors; consequently,
information about their movement cannot be acquired directly. However, once they have beenconnected to a motor, their movement can be estimated using sensor information from the servo
motor. Simulation software was employed to analyze the torque conditions of the bearing andnut corresponding to different motor torques, currents, and stator temperatures under normal
preload conditions; sensitivity and regression analyses were then performed. The results revealed
that the bearing and nut torque ratio could be expressed as a polynomial of the motor torque;thus, the motor torque obtained through servo feedback could be split into bearing and nut
torques (as shown in Fig. 6):
rBN  CBN 3 M 3  CBN 2 M 2  CBN 1 M  CBN 0 ,(8)where rBN is the nut torque τN divided by the bearing torque τB, CBNi is coefficient i of the torqueratio polynomial, and τM is the motor torque. The machine bearings could be divided into thefront and back bearings, and their torques could be calculated separately by decoupling thebearings by the same method.
Once the motor torque had been split into the bearing and nut torques, the status of the
bearing and nut was estimated. According to bearing torque theories, the preload value of the
bearing can be estimated from the actual machine bearing torque and used in fault diagnoses;
the possibility of failure due to a reduction in bearing preload or a sharp increase in friction
caused by wear and tear on the bearing could be determined. Moreover, on the basis of the
bearing torque status, machining businesses can increase or decrease the cutting depth tomaximize the machining efficiency and prevent damage to components. Regarding temperature(a)Fig. 5.

(b)(Color online) Motor temperature graphs: (a) surface temperature and (b) stator temperature.

Sensors and Materials, Vol. 36, No. 9 (2024)

Fig. 6.

3831(Color online) Relationship between motor torque and bearing-to-nut torque ratio.

predictions, by using bearing heat effect simulation and analysis technology, the current bearing
heat could be calculated from the bearing torque and added together with the previously
accumulated bearing heat to determine the total bearing heat. Predictions of bearing temperature
can be employed in displacement prediction and monitoring, improving the accuracy of amachine tool. Sensitivity analysis showed that the relationship between the initial bearing
temperature and the stator temperature could be expressed as
TBearing  CSB1Tstator  CSB 0 ,(9)where TBearing is the initial bearing temperature and CSBi is the ith-order constant in therelationship between the bearing and the motor stator.
The total heat generation of the bearing is

H B  H B 1  CBH   H' B  CBH  ,(10)

H' B  CHB' B nB ,(11)

where HB is the cumulative heat of the bearing, H'B is the current bearing heat, τB is the bearing
torque, nB is the rotational speed of the bearing, CBH is the regression coefficient of the
cumulative bearing heat at each regular sampling time until the total heat is achieved, and CHB is
the coefficient of bearing heat at the time of sampling. The values of these coefficients could beobtained through regression analysis. When the machine sampling frequency was not consistent
with that in the regression analysis (as shown in Fig. 7), CBH had to be adjusted using the ratio of
the two sampling frequencies. The bearing temperature could then be calculated as
TBearing  CBH 1H B  CBH 0 ,where CBHi is the ith-order constant of the bearing heat and temperature.

(12)

3832

Sensors and Materials, Vol. 36, No. 9 (2024)

(a)

(b)

Fig. 7. (Color online) Relationship between bearing heat and temperature: (a) stator temperature and (b) total
bearing heat.

The process of detecting the nut status is similar to that of bearing status monitoring. (1)First, the nut torque was decoupled from the motor torque of the servo drive, and the preload
value was obtained using nut torque theories. This preload value was employed to determine
whether the status was abnormal and to offer suggestions for adjustments to the cutting depth
parameters. (2) Temperature predictions involved the use of nut heat effect simulation andanalysis technology: the current nut heat was calculated from the nut torque and added together
with the previously accumulated nut heat to determine the total nut heat. Predictions of nut
temperature can be used in displacement prediction and monitoring to improve the accuracy of amachine tool. The sensitivity analysis results and regression analysis formulae for nut
temperature were similar to those for bearing temperature.
3.3

Estimation of transmission shaft straightness and backlash

A transmission shaft (also known as a linear or feed axis) primarily comprises a motor, afront bearing, screws, nuts, and a back bearing. The motor rotates and drives the screws
supported by the front and back bearings, resulting in the linear motion of the nuts on the screw
and the moving platform above them. The movement of these components generates heat, which
is transferred to the structure through heat conduction. The resulting heat deformation of thestructure causes slight deviations in the horizontal and vertical directions of the moving platform
while it is moving, and these deviations reduce machining precision. Currently, most machining
businesses conduct regular shutdowns for maintenance and repairs, during which they use laserinterferometers to measure the linear movement deviation of moving platforms. However, suchoffline measurements do not enable the immediate detection and correction of abnormalities,
and a large number of defective products are thus produced before the deviations have been
discovered. Additionally, laser interferometers are expensive, and operators of these devices
must receive training on them. Most machining businesses cannot afford the associated in-houseequipment and staff and therefore outsource this work; consequently, when an abnormality

Sensors and Materials, Vol. 36, No. 9 (2024)

3833

occurs, a plant must be shut down until it has been inspected by the contracted service provider.
To address this issue, thermal fluid–solid coupling analysis was employed in this study toestimate the linear deviations of a transmission shaft, with the temperature estimation
technology described in the previous section employed to analyze the impact of component
heating on the deformation of a transmission shaft structure. In the simulation analysis, first, thetransmission shaft was segmented into multiple nodes, and the amount of deformation of eachnode under various movement conditions was simulated and predicted separately. Horizontal
and vertical changes in axis straightness were analyzed in accordance with the geometrical
product specification standard ISO 1101. The proposed approach overcomes the issue of productdefects caused by excessive straightness changes due to the inability of machines to dynamically
predict the straightness changes caused by thermal displacement.
Once large amounts of simulation data had been gathered and the data had been validated
against laser interferometer measurements, sensitivity analysis was performed on the simulationand measured data. The results indicated that the vertical and horizontal straightness changes
could be expressed as functions of the motor and front and back bearings. This is because themotor and bearings are directly connected to the structure (whereas the screws and nuts are only
indirectly connected through the bearings), and the heat can thus be directly conducted to thestructure, producing thermal deformation. The equations are as follows:
3

3

3

j 1

j 1

j 1

3

3

3

j 1

j 1

j 1

 Hi  CHFBijTFBearing j  CHBBijTBBearing j  CHMijTMotor j  CHj ,Vi  CVFBijTFBearing j  CVBBijTBBearing j  CVMijTMotor j  CVi ,

(13)
(14)

where δHi and δVi represent the horizontal and vertical straightness deviations of node i,
respectively; CHFBij and CVFBij are the coefficients of the impact of the front bearing temperatureon the jth-order horizontal and vertical straightness deviations of node i, respectively; CHBBij and
CVBBij are the coefficients of the impact of the back bearing temperature on the jth-orderhorizontal and vertical straightness deviations of node i, respectively; CHMij and CVMij are thecoefficients of the impact of the motor temperature on the jth-order horizontal and verticalstraightness deviations of node i, respectively; CHj and CVi are the constant coefficients of thehorizontal and vertical straightness deviations, respectively; TFBearing is the temperature of thefront bearing; TBBearing is the temperature of the back bearing; and TMotor is the temperature of
the motor. The estimation model is illustrated in Fig. 8.
Regarding backlash in the transmission shaft, wear from the prolonged use of a machine tool
results in the deformation of the backlash, compromising the machining accuracy. Presently,
most inspections are conducted using laser interferometers, which also involve the risks ofmachining defects and delayed repairs, similar to those of straightness compensation. To address
this issue, a backlash detection method that employs servo feedback data to determine thebacklash of a transmission shaft was developed. First, reciprocating movement commands were
given to the transmission shaft; this was begun with the minimum movement unit, and the3834

Sensors and Materials, Vol. 36, No. 9 (2024)

Fig. 8.

(Color online) Model for estimating straightness changes in the transmission shaft.

movement range was then gradually expanded. The results demonstrated that when the
movement command was smaller than the backlash, only the motor rotated, and the moving
platform on top of the transmission shaft was not driven. Consequently, the motor current
remained low. When the movement range was greater than the backlash, the moving platform
began to move, which caused the motor current to increase or decrease depending on the
direction of the movement. This enabled the detection of the transmission shaft backlash under
nonmachining conditions and the inference of the backlash value for different rotational speeds.
The proposed approach reduces the backlash measuring time from the 15 min required whenusing a laser interferometer to below 10 min while also improving machining precision. The
current under the reciprocating movement is illustrated in Fig. 9.
3.4

Estimation of rotational axis thermal elongation

Another key component in a machining center is the rotational axis, which may constitute aspindle or rotating platform. The interior of the rotating axis mainly comprises transmission
components such as a motor, bearings, or nuts, and the backlash of each component can be
estimated and compensated by the methods described in Sect. 2.3. Whereas the transmission
shaft transmits linear movement, the rotational axis produces rotational movement; therefore,
the thermal deformation of the rotational axis primary takes the form of axial elongation. The
amount of deformation affects the parameters for correcting the machine tool length. If thermal
elongation of the rotational axis is not compensated in a timely manner, finished workpieces will
be larger or smaller than the target size, depending on whether the rotational axis has elongatedor shortened. Currently, most machining businesses ensure that a rotational axis is thermallystable (its elongation has a certain stable value with only microscale changes being possible) by
warming up the machine first (e.g., through continuous rotation for 30 min or longer) and thenmeasuring the tool length and using the controller to compensate for this length to maintainmachining accuracy. However, if a machine has been on standby for a long period (for reasons
such as workers going on a break or changing molds), the machine must be warmed up again,Sensors and Materials, Vol. 36, No. 9 (2024)

Fig. 9.

3835

Motor current during backlash inspection

which wastes time and compromises production capacity. To address this issue, we developed atechnology for estimating the thermal elongation of the rotational axis. The heat dissipation andthermal displacement of a rotational axis were analyzed by examining the heat generated by a
motor and bearings; finite element analysis software was then employed to establish therelationship between the servo feedback and the thermal displacement. The proposed technology
enables machining businesses to periodically estimate the elongation of the rotational axis andthus predict the thermal displacement of the shafts; with this information, the businesses canrapidly compensate the tool length and improve machining accuracy.
Large amounts of simulation data were gathered, and these data were verified against eddycurrent detector measurements. Sensitivity analysis was then performed on the simulation andmeasured data. The results revealed that the thermal displacement of the rotational axis could be
expressed as a function of the motor’s load, rotational speed, and temperature difference: R  CRT T  CRM S M  CRL LM  CRC ,(15)

where δR is the thermal elongation of the rotational axis; CRT, CRM, CRL, and CRC are constants
derived through regression analysis; ΔT is the difference between the current stator temperatureand the stator temperature at the time of tool calibration; and LM is the motor load. Entering dataon the motor’s rotational speed, load, and temperature into Eq. (15) enabled the calculation of theamount of elongation. The accuracy of the thermal elongation of rotational axis is shown in Fig.
10.
3.5

On-site β-site system validation

To validate its appropriateness, β-site validation was conducted by introducing the proposed
technology in an actual machining plant that performs turbine bush milling. The test machining
process is illustrated in Fig. 11. Each hour, the manufacturer can produce six turbine bushings on3836

Sensors and Materials, Vol. 36, No. 9 (2024)

Fig. 10. (Color online) Relationship between rotational axis temperature and thermal displacement.

Fig. 11. (Color online) Machining process of the plant used for β-site validation.

each machine. However, Taiwan’s declining birth rate has led to a labor shortage and an inability
to pass on production line experience. Consequently, the manufacturer hoped to improve theirmachining accuracy and efficiency through the introduction of digital technologies and theprevention of sudden failures. The verification conditions in this study are shown in Table 1, andthe results are shown in Table 2. Using the results in Table 2 for regression analysis, the predicted
and actual thermal displacements of the rotational axis were obtained, as shown in Fig. 12.
The equipment status monitoring and precision estimation technology developed in thisstudy was introduced to the machining process in the following manner.
• Routine machine warmup monitoring: An onsite operator revised the routine machine
warmup task so that it would be executed by the transmission and rotational axis statusmonitoring module developed in this study. The software module automatically monitored
the statuses of the transmission and rotational axis and provided a fault warning system that
could prevent sudden failures. Furthermore, the transmission shaft backlash was calculated
during the machine warmup process, and the compensation values were displayed on thehuman–machine interface, enabling managers to decide whether parameters should beentered into the machine controller.
• Trial machining and adjustments: During the cutting process, the on-site manager ran thesoftware module to monitor the machine tool status. Once the machining program wasSensors and Materials, Vol. 36, No. 9 (2024)

3837

Table 2
Experimental results.

Operation conditions
andthermal deformations

Operation 3 hStop 1 h
Run 1.5 h
1 h Lunch break errors(μm)
Max. (μm)
Min. (μm)
Difference (μm)

1
−21
−26
−28

2
−33
−19
−26

3
−34
−37
−45

5

14

3

0
−29
29

0
−33
33

0
−45
45

Fig. 12. (Color online) Predicted and actual thermal displacements of the rotational axis.

complete, the software module displayed the recommended adjustments to the depth of cut(to be applied to the rough cutting). The manager could calibrate the machining program inaccordance with the displayed results to improve the machining efficiency.
• Machining process monitoring: During the machining process, the developed softwaremodule was kept running so that it could automatically monitor changes in transmission shaft
straightness and thermal elongation in the rotational axis. The statuses of the axis weredisplayed on the software interface, enabling managers to enter the necessary parameters into
the machine tool controller to compensate for any thermal displacements and thus improvethe machining accuracy.
The accuracy of the model estimations was verified by employing actual machining practices
with a five-axis machining center developed by the Industrial Technology Research Institute;instruments such as thermometers, load cells, and a laser interferometer were irregularly
employed to take measurements and verify the accuracy of the estimations. Using the elongationof the rotational axis as an example, during validation, the controller provided feedback about
the rotational speed, torque, and stator temperature. The axial thermal elongation history was
taken into consideration when the temperature and thermal elongation of the rotational axis werebeing estimated, and the actual thermal displacement was derived from the displacement

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Sensors and Materials, Vol. 36, No. 9 (2024)

measurements and compared with the predictions. Lastly, all the measurements and predictions
were analyzed to determine the coefficient of determination (R2), which described the accuracyof the model estimations. The results are illustrated in Fig. 9.
The estimation accuracy for each technology is detailed in Table 3.
The experimental results indicate that when the sensor signal is close to the estimation target
and the sensing data can be used to predict the state, a higher estimation accuracy can beachieved (such as for motor temperature estimation). However, if more than two sets ofregression equations are required for state prediction, the prediction accuracy decreases as thenumber of equations increases (such as for bearing and nut temperature estimation). Practically,
owing to mechanical design constraints, it is often difficult to place sensors directly at themeasurement location, making it hard to detect the state of parts. Compared with the current
detection difficulties, we provide a simple method to directly estimate the state of parts that are
difficult to measure using servo feedback, thereby preventing unexpected failures. Additionally,in this study, we primarily use multiple regression analysis to conduct sensitivity analysis on
multiple input and one output parameters from a small number of experiments and a large
amount of finite element analysis simulation results, producing corresponding regression
equations. According to the equations obtained in this study, state estimation through multiple
linear regression equations can generally achieve an estimation accuracy of more than 90%.
However, practically, the linear regression analysis method cannot be applied to all machines.
The thermal deformation prediction equations of machine tools are related to machine design.
Considering conditions such as thermal symmetry, the thermal deformation equations canusually be simplified into linear regression equations. If the thermal effects are not considered in
the machine design, it is generally difficult to achieve good estimation results using regression
analysis. Many researchers have also invested in the prediction and compensation methods forthe thermal deformation of such types of machines using neural networks such as LSTM, GRU,
and RNN. However, the estimation calculations are much more complex and cannot beembedded into the machine tool controller for real-time compensation. The results of our study
also align with those in Okuma’s technical white paper:(21) regression analysis is an effective
method for thermal compensation, and if the results are inaccurate, it may indicate a problem
with the machine tool design. Therefore, the results of this study further demonstrate theeffectiveness of regression analysis in machine tool thermal compensation and a thermalcompensation method that can be embedded into the machine tool motion controller isdeveloped, which will be introduced into end-processing plants for actual machining
verification. The benefits to the machining business from the introduction of these technologies
can be summarized as follows.
Table 3
Status monitoring accuracy
Estimation target
Motor temperature
Bearing temperature
Nut temperature
Transmission shaft straightness
Transmission shaft backlash
Rotational axis thermal elongation

Estimation accuracy
R2 ≈ 0.92
R2 ≈ 0.88
R2 ≈ 0.90
Horizontal straightness R2 ≈ 0.93
Vertical straightness R2 ≈ 0.94
R2 ≈ 0.97
R2 ≈ 0.92

Sensors and Materials, Vol. 36, No. 9 (2024)

3839• The validation of machining accuracy and yield rate was performed through random
inspections of the turbine bushings produced when following the original quality control
protocols of the collaborating manufacturer. The original tolerance was approximately 0.05
mm. Following the introduction of the thermal displacement estimation technology, thecompensation was improved to 0.03; furthermore, the tolerance was exceeded for no morethan one item per 100 samples. Hence, the technology was shown to effectively improvemachining accuracy and yield while addressing the impact of misaligned lubrication holes on
the lubrication of turbine bushings.
• Regarding adjustments to the machining parameters, the machining center status andcomponent stress could be automatically estimated using status estimation technology and avisual interface, and recommendations for the maximum cutting depth could be provided.
The user could modify the machining program in accordance with the recommendation, andthe number of trial cuts was reduced by more than 30%.
• No unforeseen shutdowns occurred during the technical validation period of this study.
Furthermore, the equipment status detection performed by the warmup program and using
the technology developed in this study reduced the time taken to inspect three-axis milling
beds by 60%.

4.

Conclusions

In this study, systems that use servo feedback data were developed for status estimation,
precision estimation, and the compensation of the machine tool transmission and rotational axes.
The proposed technologies do not require the installation of sensors and can perform estimations
using only the servo feedback information obtained from the machine tool controller. Comparedwith existing sensorless estimation techniques, this approach improves the estimation accuracy,
avoids incorrect estimations due to sudden changes in machine tool status, and eliminates theneed for additional sensor installations at specific positions, which would require modifications
to the mechanical design. The proposed method was practically introduced into a β-site formachining verification. The verification results indicate that, with the proper mechanical designof the machine tool, the accuracy of estimating mechanical part temperatures and thermal
deformation through regression analysis can reach a value above 88%. This method is easier tointegrate into the machine tool controller for real-time compensation than existing neuralnetwork methods, and the results are consistent with those in Okuma’s technical white paper.
The validation results indicate the following benefits to machining businesses:• Improving the value added to products: Machining accuracy can be improved by equipping
machine tools with intelligent machining application functions to carry out efficient andintelligent machining and production; in addition, defect rates can be reduced, and trial
machining parameter adjustment and machine status detection times can be shortened.
• Establishing smart manufacturing capabilities: Small-batch, diverse, and customized
requirements will become the norm for customer orders in the future, and the stability andefficiency of machining will affect manufacturing capabilities. Establishing smart
manufacturing capabilities by using the status detection technologies developed in this study

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Sensors and Materials, Vol. 36, No. 9 (2024)

would enable the digital and visual management of the equipment status. As well as reducing
time-consuming and inaccurate manual operations, the developed technologies enable
quality monitoring, production progress querying, and customer feedback in real time.
Overall, these technologies can effectively improve product quality and lead times while
lowering product costs, thereby improving a company’s competitiveness.

Acknowledgments
The authors gratefully acknowledge the financial support provided to this study by the
National Science and Technology Council of Taiwan under Grants NSTC 113-2221-E-167-016MY3 and NSTC 113-2222-E-167 -001 -MY2.

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3841

About the Authors
C.K. Huang received his Ph.D. degree from the Department of MechanicalEngineering at National Taiwan University of Science and Technology in 2016
and subsequently joined the Industrial Technology Research Institute (ITRI)
to conduct research on smart manufacturing. Since 2021, he has served as an
R&D manager at the Intelligent Machinery Technology Center of ITRI. In
2024, he transitioned to National Chin-Yi University of Technology, where heholds the position of assistant professor. His current research interests include
the application of robotic arms, manufacturing accuracy, and the control ofsmart manufacturing. (CKHuang@ncut.edu.tw)
Chun-Hao Chen obtained his master's degree and graduated from the
Department of Mechatronic Engineering, National Taiwan Normal University,
Taiwan in 2006. He is currently studying in the doctoral program at National
Chin-Yi University of Technology. His research interests are in digital signal
processing, industrial robot application, and machine tool design technology.
(jical-chen@turvo.com.tw)
Kun-Ying Li received his B.S. degree from the Department of Bio
Mechatronics Engineering, National Chung Hsing University and M.S. degreefrom the Department of Mechanical Engineering at National Chung Cheng
University, Taiwan, in 2007. From 2007 to 2020, he was an engineer with theIntelligent Machinery Technology Center in ITRI. He received his Ph.D
degree from National Chin-Yi University of Technology, Taiwan, in 2020. He
has been an associate professor in the Intelligent Automation Engineering
Department of National Chin-Yi University of Technology, Taiwan, since2020. His research interests include thermal errors of machine tools, design for
precision machinery, reliability engineering, and applications. He holds 15
patents in machine tools. (likunying@ncut.edu.tw)		Shih-Jie Wei received his Master's degree from the Institute of Mechanicaland Electromechanical Engineering at National Formosa University in 2012.
He has been working as an engineer at the Industrial Technology ResearchInstitute (ITRI) since 2012. His research interests include hydrostatic bearing
technology, reliability analysis, and thermo-fluid–solid coupling technology.
He holds nine patents in the field of mechanical engineering.
(itriA10390@itri.org.tw)